Let $X$ be a $\mathbb{ Q}$-factorial klt projective variety admitting an int-amplified endomorphism $f$, i.e., the modulus of any eigenvalue of $f^*|_{ \text{ NS}(X)}$ is greater than $1$. We prove Kawaguchi-Silverman conjecture for $f$ and also any other surjective endomorphism of $X$: the first dynamical degree equals the arithmetic degree of any point with Zariski dense orbit. This generalizes an early result of Kawaguchi and Silverman for the polarized $f$ case, i.e., $f^*|_{ \text{ NS}(X)}$ is diagonalizable with all eigenvalues of the same modulus greater than $1$.
Categories: math.AG math.DS math.NT